Is an independent resident allowed to disrespect a CNA?

What type of "disrespect" are you talking about?
I think disrespect of any type should not be tolerated.
Particularly if the person is in Independent living and they have no cognitive declines. If they are fully aware of what they are doing and or saying then I would say no they should not be "allowed" to disrespect anyone.
If they are told that the behavior is unacceptable and it continues then I can see where they may be asked to find other housing. (check the terms of agreement and resident rules I am sure there is something in there)
If the person has been diagnosed with dementia that is a different story since "filters" get dropped. And if the person has dementia then their care is beyond Independent Living and they may be asked to transfer to a facility that is better able to care for them.

What do you mean "allowed" to?

Are you asking that they be reprimanded?

In what way did this resident insult the CNA?

Does the resident have dementia?

Why is there a CNA in an Independent Living Facility?

ReaAllen412, we need more information to be able to help you with this question. Such as what do you mean by independent resident? What are the health issues with said person. Is that person living at home, or in a senior facility in Independent Living? What type of disrespect is this person giving?